In a raucous Elland Road atmosphere, two goals in five first-half minutes saw the hosts race into a 2-0 lead with Chelsea, who finished with 10 men, unable to cope with the intensity.
The result meant Leeds have now picked up seven points from their opening three games.
The hosts started well when Edouard Mendy made a mess of a routine clearance, allowing Brenden Aaronson to capitalise just after the half-hour mark.
The U.S. forward took the ball from the Chelsea goalkeeper’s feet and dribbled into an empty net.
Chelsea were unfortunate to be one goal down after missing some early chances, but soon after the opener, they found themselves two goals behind.
This was when Rodrigo emphatically headed in Jack Harrison’s delicate free-kick to earn the Spaniard his fourth Premier League goal of the season.
In a commanding performance, Leeds added a third in the 69th minute — Daniel James’ cross was nodded down by Rodrigo into the path of Harrison, who fired past Mendy to make the lead comfortable.
“It was the best performance since I have been here,” Marsch said. “You are starting to see a bunch of players who understand their role, some in the form of their lives.
“Our way of playing dictated the match. We made them make mistakes.
“These quality players can pass the ball all day if we give them time. We wanted to make them uncomfortable, and today we did.”
Thomas Tuchel was on the touchline as his ban for last week’s confrontation with Tottenham boss Antonio Conte was suspended.
Marsch, who had said that Tuchel shouldn’t be allowed on the bench, told reporters before the game:
“I don’t think it’s right that he should be able to appeal [his red card], but whatever, he’s on the bench — let’s play the game.”
But the Chelsea manager’s involvement didn’t spur Chelsea to a comeback, as summer signing Kalidou Koulibaly was sent off five minutes from time and Tuchel’s side plummeted to their first defeat of the season.
“We scored an own goal and conceded from a set piece,” Chelsea coach Thomas Tuchel said.
“The defeat is nothing to do with pressing, nothing to do with running less kilometres and nothing to do with the style of Leeds.
“We were able to be the better team. But then it was 2-0 and our body language was not like it was in the last match.
“I don’t see the connection that we lost to the style of Leeds. We knew it was coming.” (Reuters/NAN)